AP Calculus BC Multiple Choice 1998 Questions - Practice Exam (pdf)

Part A, Q1 - 28

Part B, Q76 - 92

- What are all values of x for which the function f defined by f(x) = x
^{3}+ 3x^{2}- 9x + 7 is increasing? - In the xy-plane, the graph of the parametric equations x = 5t + 2 and y = 3t, for −3 ≤ t ≤ 3 , is a line segment with slope
- The slope of the line tangent to the curve
- Antiderivative
- If f and g are twice differentiable and if h(x) - f(g(x)) then h''(x) =
- The graph of y = h(x) is shown above. Which of the following could be the graph of y = h'(x)?
- Antiderivative
- If dy/dx = sinxcos
^{2 x} - The flow of oil, in barrels per hour, through a pipeline on July 9 is given by the graph shown above. Of the following, which best approximates the total number of barrels of oil that passed through the pipeline that day?
- A particle moves on a plane curve so that at any time t > 0 its x-coordinate is t
^{3}- t and its y-coordinate is (2t - 1)^{3}. The acceleration vector of the particle at t = 1 is - If f is a linear function and 0 < a < b
- If f(x) =
- The graph of the function f shown in the figure above has a vertical tangent at the point (2,0) and horizontal tangents at the points (1, -1) and (3,1). For what values of x, −2 < x < 4, is f not differentiable?
- What is the approximation of the value of sin 1 obtained by using the fifth-degree Taylor polynomial about x = 0 for sin x ?
- Antiderivative
- If f is the function defined by f(x) = 3x
^{5}- 5x^{4}, what are all the x-coordinates of points of inflection for the graph of f? - The graph of a twice-differentiable function f is shown in the figure above. Which of the following is true?
- Which of the following series converge?
- The area of the region inside the polar curve r = 4sin θ and outside the polar curve r = 2 is given by
- When x = 8 , the rate at which
- The length of the path described by the parametric equations
- Limits
- Let f be a function defined and continuous on the closed interval [a, b]. If f has a relative maximum at c and a < c < b , which of the following statements must be true?
- Shown above is a slope field for which of the following differential equations?
- Antiderivative
- The population P(t) of a species satisfies the logistic differential equation
- Taylor series that converges to f(x)
- Limits

76. For what integer k, k > 1, will both

77. If f is a vector-valued function defined by

78. The radius of a circle is decreasing at a constant rate of 0.1 centimeter per second. In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second?

79. Let f be the function given by

80. Let R be the region enclosed by the graph of

81. Derivative

82. If f(x) = g(x) + 7 for 3 ≤ x ≤ 5

83. The Taylor series for ln x , centered at x = 1

84. What are all values of x for which the series

85. The function f is continuous on the closed interval [2,8] and has values that are given in the table above. Using the subintervals [2,5 , 5,7 , ] [ ] and [7,8], what is the trapezoidal approximation of

86. The base of a solid is a region in the first quadrant bounded by the x-axis, the y-axis, and the line x + 2y = 8 , as shown in the figure above. If cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid?

87. Which of the following is an equation of the line tangent to the graph

88. Let g(x) =

89. The graph of the function represented by the Maclaurin series

90. A particle starts from rest at the point (2,0) and moves along the x-axis with a constant positive acceleration for time t ≥ 0 . Which of the following could be the graph of the distance ( ) s t of the particle from the origin as a function of time t?

91. The data for the acceleration ( ) a t of a car from 0 to 6 seconds are given in the table above. If the velocity at t = 0 is 11 feet per second, the approximate value of the velocity at t = 6 , computed using a left-hand Riemann sum with three subintervals of equal length, is

92. Let f be the function given by

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